The present invention relates to circuit simulators, and more particularly, to circuit simulators for modeling high frequency planar circuits and interconnect structures utilizing the method of moments.
Integrated circuits for use at high frequencies often include high frequency interconnections such as coupled transmission lines, junctions, spirals, via""s through ground planes, etc. Precise characterization of such high-frequency interconnections is very important for circuit simulation and optimization purposes. Various numerical full-wave electromagnetic analysis techniques have been used to characterize these interconnect structures. Solutions to the characterization problem based on solving Maxwell""s electromagnetic (EM) equations using the method of moments (MoM) are commercially available and are well suited to the problem of characterizing planar circuits consisting of planar metallization layers embedded in a multilayered dielectric medium. Applications of such planar circuits are found in microwave monolithic integrated circuits (MMICs), printed circuit boards (PCBs), multichip modules (MCMs), hybrid microwave integrated circuits (MICs) and radio frequent integrated circuits (RFICs).
Methods based on finite element algorithms are also known to the art. However, these methods are better suited for simulating arbitrary three-dimensional structures.
The widespread use of EM simulators is hampered by two problems. First, EM simulators are very computer resource intensive. Hence, such simulators are not easily integrated into more general CAD systems. Second, a basic understanding of the underlying principles and technologies of EM simulators is a prerequisite for generating successful interconnect designs using such simulators. The designer using the EM tool must have some understanding of the underlying method of moments technology. The user himself has to initialize the mesh parameters (number of cells/wavelength, number of cells/transmission line width, edge meshing on/off, etc.). Setting these parameters is always a trade off between simulation accuracy and simulation speed. The larger the number of cells, the more accurate the solution, but the longer it will take to obtain this solution.
Setting the correct tradeoff is complicated by the lack of accuracy information. The state-of-the-art method of moments technology is not capable of giving the user any feedback on the accuracy of the solutions with respect to the discretization errors. Nor does it provide the user with any feedback regarding the relationship between the initialization of the mesh parameters and the discretization error in the solution. Currently, users of planar EM tools verify the accuracy by refining the mesh, resimulating and looking at the differences in the solutions. The burden to specify the mesh parameters and to verify the mesh accuracy is left to the user. Only EM experts with MoM expertise are able to successfully initialize the mesh parameters for a wide range of structures and obtain accurate results within a reasonable design time.
Adaptive solution refinement (ASR) technologies have been used in combination with the finite element based EM simulators. These systems utilize an algorithm that adapts and refines the mesh automatically in consecutive iterations and thereby reduce the discretization error on the output S-parameters. The mesh refinement is driven by an a-posteriori error estimation technology. Starting from an initial solution on an initial mesh, the algorithm evaluates the discretization errors and calculates error estimates. These error estimates indicate the regions in the solution domain where the discretization error is expected to be the largest. The mesh is adapted and refined only in those areas with the largest error. A new solution is built using the refined mesh and convergence of the output parameters is checked. This process is repeated until the convergence criterion is satisfied.
Unfortunately, application of such adaptive solution refinement (ASR) methods to the method of moments analysis of planar circuits is not straightforward. In finite element methods, the matrix that must be inverted is computationally cheap to create and is highly sparse. In addition, computation of the discretization error is also computationally cheap. As a result, making adaptations and refinements to the mesh can be readily accomplished without using much additional computational resource. In the method of moments, the matrix is dense and filling and solving the matrix is very expensive in terms of computer resources. Also, the integral equation operator representing Maxwell""s equations is ill conditioned, and hence, the use of faster iterative matrix inverting techniques is prohibited.
Furthermore, the ASR techniques currently in use do not allow the computational work performed at one mesh level to be re-used at the next higher mesh level. Hence, such methods are computationally inefficient.
In addition, finite element ASR techniques as currently implemented utilize an error estimation driven adaptation of the mesh that is performed only at one frequency. The final mesh at this frequency is reused for simulations at all the other frequency points. In the case of resonance structures, the optimal final mesh obtained at a frequency not in the neighborhood of the resonance frequency can be much less optimal for modeling at the resonance frequency as the field distributions can change quite drastically when resonance occurs. In fact, some resonance""s can be missed completely by less optimal finite element methods.
Broadly, it is the object of the present invention to provide an improved method of moments EM simulator.
It is a further object of the present invention to provide a MoM simulator that automatically refines the mesh size used in the computation until the simulation converges to a predetermined accuracy.
It is a still further object of the present invention to provide a MoM simulator that performs mesh refinement at multiple frequencies.
It is yet another object of the present invention to provide a MoM simulator that recaptures the computational work expended in prior mesh computations at each successive refinement of the mesh.
These and other objects of the present invention will become apparent to those skilled in the art from the following detailed description of the invention and the accompanying drawings.
The present invention is a method for operating a computer to determine the electrical characteristics of a passive planar structure. The method starts by defining a first mesh on the structure. The first mesh divides the structure into polygons. A surface current is defined in the structure as a first weighted sum of a first set of basis functions. The weights of the first basis functions in the first weighted sum are calculated by solving Maxwell""s equations. The mesh is then refined by dividing each polygon into a plurality of sub-polygons. The surface current in the sub-polygons is defined as a second weighted sum of a second set of basis functions. The second set of basis functions includes the first set of basis functions and a plurality of extension basis functions representing the additional degrees of freedom introduced by the refined mesh. The weights of the second basis functions in the second weighted sum are calculated by solving Maxwell""s equations. In the preferred embodiment of the present invention, the extension basis functions include a capacitative set of basis functions representing the capacitative contribution of the sub-polygons and an inductive set of basis functions representing the inductive contributions of the sub-polygons. The calculation of the weights in the second basis functions preferably includes solving Maxwell""s equations for each polygon in the first mesh structure assuming that the currents in all other polygons in the first mesh structure remain unchanged. The step of defining the surface current in the second set of basis functions preferably includes estimating the contribution of each basis function in the capacitative and inductive sets of basis functions and removing those capacitive basis functions whose contributions are less than a capacitative threshold value and those inductive basis functions whose contributions are less than an inductive threshold value.